Cascade equations and hadronic interactions at high energies

The new matrix form of cascade equations is convenient to discuss numerical properties and to investigate the role of hadrons and phase-space for atmospheric leptons. Precision is often limited by hadronic interactions models. I improved the event generator DPMJET-III using experimental data including the LHC. A specific curvature in charged-particle multiplicity distributions raised questions about elastic scattering amplitude and the black disk limit at LHC energies.